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<div class="section" id="metafunctions">
<h1><a class="toc-backref" href="../refmanual.html#id1510">Metafunctions</a></h1>
<p id="label-metafunctions">The MPL includes a number of predefined metafunctions that can be roughly
classified in two categories: <cite>general purpose metafunctions</cite>, dealing with
conditional <a class="reference internal" href="./type-selection.html">type selection</a> and higher-order metafunction <a class="reference internal" href="./invocation.html">invocation</a>,
<a class="reference internal" href="./composition-and-argument-binding.html">composition</a>, and <a class="reference internal" href="./composition-and-argument-binding.html">argument binding</a>, and <cite>numeric metafunctions</cite>,
incapsulating built-in and user-defined <a class="reference internal" href="./arithmetic-operations.html">arithmetic</a>, <a class="reference internal" href="./comparisons.html">comparison</a>,
<a class="reference internal" href="./logical-operations.html">logical</a>, and <a class="reference internal" href="./bitwise-operations.html">bitwise</a> operations.</p>
<p>Given that it is possible to perform integer numeric computations at
compile time using the conventional operators notation, the need for the
second category might be not obvious, but it in fact plays a cental role in
making programming with MPL seemingly effortless. In
particular, there are at least two contexts where built-in language
facilities fall short <a class="footnote-reference" href="#portability" id="id820">[3]</a>:</p>
<ol class="arabic simple">
<li>Passing a computation to an algorithm.</li>
<li>Performing a computation on non-integer data.</li>
</ol>
<p>The second use case deserves special attention. In contrast to the built-in,
strictly integer compile-time arithmetics, the MPL numeric metafunctions are
<em>polymorphic</em>, with support for <em>mixed-type arithmetics</em>. This means that they
can operate on a variety of numeric types — for instance, rational,
fixed-point or complex numbers, — and that, in general, you are allowed to
freely intermix these types within a single expression. See <a class="reference internal" href="./numeric-metafunction.html">Numeric Metafunction</a> concept for more details on the MPL numeric infrastructure.</p>
<!-- The provided `infrastructure`__ allows easy plugging of user-defined numeric
types
Naturally, they also , meaning that you can perform a computation on the
arguments of different types, and the result will yeild the largest/most general
of them. For user-defined numeric types, they provide an `infrastructure`__ that
allows easy plugging and seemless integration with predefined library
types. details.

__ `Numeric Metafunction`_ -->
<p>To reduce a negative syntactical impact of the metafunctions notation
over the infix operator notation, all numeric metafunctions
allow to pass up to N arguments, where N is defined by the value of
<a class="reference internal" href="./limit-metafunction-arity.html">BOOST_MPL_LIMIT_METAFUNCTION_ARITY</a> configuration macro.</p>
<table class="docutils footnote" frame="void" id="portability" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#id820">[3]</a></td><td>All other considerations aside, as of the time of this writing
(early 2004), using built-in operators on integral constants still often
present a portability problem — many compilers cannot handle particular
forms of expressions, forcing us to use conditional compilation. Because MPL
numeric metafunctions work on types and encapsulate these kind of workarounds
internally, they elude these problems, so if you aim for portability, it is
generally adviced to use them in the place of the conventional operators, even
at the price of slightly decreased readability.</td></tr>
</tbody>
</table>
<ul class="toc simple" id="outline">
<li><a class="reference internal" href="./metafunctions-concepts.html" id="id1511">Concepts</a></li>
<li><a class="reference internal" href="./type-selection.html" id="id1519">Type Selection</a></li>
<li><a class="reference internal" href="./invocation.html" id="id1524">Invocation</a></li>
<li><a class="reference internal" href="./composition-and-argument-binding.html" id="id1528">Composition and Argument Binding</a></li>
<li><a class="reference internal" href="./arithmetic-operations.html" id="id1535">Arithmetic Operations</a></li>
<li><a class="reference internal" href="./comparisons.html" id="id1542">Comparisons</a></li>
<li><a class="reference internal" href="./logical-operations.html" id="id1549">Logical Operations</a></li>
<li><a class="reference internal" href="./bitwise-operations.html" id="id1553">Bitwise Operations</a></li>
<li><a class="reference internal" href="./trivial.html" id="id1559">Trivial</a></li>
<li><a class="reference internal" href="./string-operations.html" id="id1561">String Operations</a></li>
<li><a class="reference internal" href="./miscellaneous.html" id="id1563">Miscellaneous</a></li>
</ul>
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